My iPhone 2G seems to be having some major issues. When it is unplugged, it won't turn on at all. If I plug it in to the USB, it won't turn on at all. If I plug it in to the wall charger, it turns right on and shows me the apple logo, but after 5 seconds it reboots itself and keeps rebooting every 5 seconds until I unplug it, at which point it goes back to not turning on. I have left it on the charger for a few hours in the thought that it might need to be charged, but it makes no difference. Any ideas what I should do now? I am guessing that the logic board is probably OK or it wouldn't give me the logo, right? Could this be a bad comm board or a battery problem?

Any ideas you might have (besides 'get a new phone') would be appreciated.

That´s correct, there should be a missing connection within the commboard and the logic board, or within the battery and the commboard. I´ve just get an error like that and realice that without the commboard it make no diference so it´s a CB issue. (the problem I thought was when soldering the battery, the f***ng solder iron make short circuit with the grown and the red wire so... probably burn some IC or, blown some trace). I´ve read somewhere that there is a hardware patch to the commboard when it doesn´t turn on because of battery conection, but I can´t find it anymore...
First of all, try reconnecting your commboard, else you can test the voltage within red and black battery connectors. And last you can do is search this method I mentioned before, and please post it so I can try it also.
Good luck